Which of the following numbers is a multiple of 13? ${71,82,84,91,119}$
The multiples of $13$ are $13$ $26$ $39$ $52$ ..... In general, any number that leaves no remainder when divided by $13$ is considered a multiple of $13$ We can start by dividing each of our answer choices by $13$ $71 \div 13 = 5\text{ R }6$ $82 \div 13 = 6\text{ R }4$ $84 \div 13 = 6\text{ R }6$ $91 \div 13 = 7$ $119 \div 13 = 9\text{ R }2$ The only answer choice that leaves no remainder after the division is $91$ $ 7$ $13$ $91$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $91$ $91 = 7\times13 13 = 13$ Therefore the only multiple of $13$ out of our choices is $91$. We can say that $91$ is divisible by $13$.